docs: def get_active_trips_df(trip_times: DataFrame) -> DataFrame:
      """
      Count the number of trips in ``trip_times`` that are active
      at any given time.
  
      Parameters
      ----------
      trip_times : DataFrame
          Contains columns
  
          - start_time: start time of the trip in seconds past midnight
          - end_time: end time of the trip in seconds past midnight
  
      Returns
      -------
      Series
          index is times from midnight when trips start and end,
          values are number of active trips for that time
  
      """
      active_trips = (
          pd.concat(
              [
                  pd.Series(1, trip_times.start_time),  # departed add 1
                  pd.Series(-1, trip_times.end_time),  # arrived subtract 1
              ]
          )
          .groupby(level=0, sort=True)
          .sum()
          .cumsum()
          .ffill()
      )
      return active_trips